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摘要: 利用離散單元法（Discrete element method，DEM）對球形顆粒群以及非球形顆粒群的篩分過程進行了仿真并開展了實驗研究，結果表明球形和非球形顆粒的仿真與實驗中篩分效率的變化是一致的，但非球形顆粒的仿真結果與實驗結果更接近。正交設計多組模擬試驗，分析了各振動參數（振動頻率、振幅以及篩面傾角）對顆粒分布曲線、篩分效率以及物料平均運輸速度的影響規律。對正交試驗表中的數據進行多元非線性擬合，得到篩分效率與振動參數間的關系式；并在此關系式的基礎上，對振動參數進行優化設計，得到了最優振動參數且在仿真中得到了驗證。研究內容不但為高頻振網篩振動參數的設計提供了理論依據，而且為研究高頻振動系統的篩分機理提供了實驗和仿真數據支持。Abstract: The screening efficiency and average transport speed of materials are important indicators for measuring the performance of screening machinery. In recent years, few breakthroughs have been made in traditional screening machinery. As high-efficiency vibration machinery, high-frequency vibrating screens have become widely used in recent years, but the operational methods of high-frequency vibrating mesh screens are relatively unique: the screen box is fixed and the screen is vibrated at a high frequency. Despite its wide use, there are relatively few studies about the materials movement law and screening characteristics of high-frequency vibrating screen. In this study, a discrete element method (DEM) was used in a simulation of the screening process of the spherical and nonspherical particle groups, and an experimental study was also conducted. The results show that changes in the screening efficiency in the simulation of spherical and nonspherical particles are consistent with those observed experimentally, but the simulation results for the nonspherical particles were closer to those obtained in the experiments. Orthogonal designs and multiple sets of simulation tests were conducted to analyze the influence of each vibration parameter (vibration frequency, amplitude and mesh inclination) on the particle distribution curve, screening efficiency, and average transport speed of the materials. Multivariate nonlinear fitting was performed on the data using the orthogonal test table, and the relationship between the screening efficiency and the vibration parameters was obtained. Based on this relationship, the optimal vibration parameters were obtained and verified in the simulation. The results obtained in this research provide a theoretical basis for the design of the vibration parameters of the high-frequency vibrating screen, and the experimental and simulation data provide support for the investigation of the screening mechanism of the high-frequency vibration system.
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圖 1 軟球干接觸模型顆粒間受力示意圖
Figure 1. Diagram of force between particles in soft ball dry contact model
圖 4 不同類型的非球形顆粒。（a）長條形顆粒；（b）三角形顆粒；（c）正方形顆粒
Figure 4. Different types of nonspherical particles: (a) strip particle; (b) triangle particle; (c) square particle
圖 5 高頻振網篩篩分實驗系統照片
Figure 5. Photograph of screening experiment system with high-frequency mesh-vibrating screen
圖 8 不同振動頻率下顆粒分布曲線
Figure 8. Particle distribution curves at different vibration frequencies
圖 9 振動頻率對篩分效率和物料平均運輸速度的影響
Figure 9. Influence of vibration frequency on screening efficiency and average transport speed of materials
圖 11 振幅對篩分效率以及物料平均運輸速度的影響
Figure 11. Influence of amplitude on screening efficiency and average transport speed of materials
圖 12 不同篩面傾角下的顆粒分布曲線
Figure 12. Particle distribution curves at different mesh inclinations
圖 13 篩面傾角對篩分效率以及物料平均運輸速度的影響
Figure 13. Influence of mesh inclination on screening efficiency and average transport speed of materials
圖 15 不同振動參數組合下的篩分效率響應面
Figure 15. Response surfaces of screening efficiencies for different combinations of vibration parameters
表 1 仿真條件與物料參數
Table 1. Simulation conditions and material parameters
Parameter name Parameter value Mesh size (length × width)/mm 450 × 225 Particle shape Spherical/Nonspherical Density/(kg?m?3) Particle: 2800; Steel: 7800 Poisson’s ratio Particle: 0.25; Steel: 0.3 Shear modulus/Pa Particle: 5 × 107; Steel: 8 × 1010 Coefficient of Restitution Particle – Particle: 0.2; Particle – Steel: 0.3 Coefficient of Static Friction Particle – Particle: 0.6; Particle – Steel: 0.4 Coefficient of Rolling Friction Particle – Particle: 0.01; Particle – Steel: 0.01 
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表 2 不同粒徑尺寸的顆粒性質
Table 2. Characteristics of particles of different sizes
Particle size/mm Property Generation speed/(kg?s?1) Particle distribution/% 1.5 Easy-to-sieve 0.015 10 2.0 Easy-to-sieve 0.015 10 2.5 Easy-to-sieve 0.015 10 3.5 Difficult-to-sieve 0.025 10 4.5 Difficult -to-sieve 0.025 10 5.0 Obstructed-to-sieve 0.01 10 6.0 Obstructed-to-sieve 0.01 10 7.0 Obstructed-to-sieve 0.01 10 8.0 Obstructed-to-sieve 0.015 10 9.0 Obstructed-to-sieve 0.015 10
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表 3 水平與因素對應表
Table 3. Correspondence of levels and factors
Level Vibration frequency/Hz Amplitude/mm Mesh inclination/(°) 1 30 0.5 20 2 35 1.0 25 3 40 1.5 30 4 50 2.0 35 5 70 2.5 40
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表 4 正交試驗結果
Table 4. Results of orthogonal tests
Group Vibration
frequency/HzAmplitude/
mmMesh inclination/
(°)Screening
efficiency/%Average transport
speed/(m?s?1)Group Vibration
frequency/HzAmplitude/
mmMesh inclination/
(°)Screening
efficiency/%Average transport
speed/(m?s?1)1 30 0.5 20 78.13 0.412 14 40 2.0 20 77.55 0.621 2 30 1.0 25 74.56 0.483 15 40 2.5 25 74.95 0.801 3 30 1.5 30 72.94 0.623 16 50 0.5 35 76.23 0.822 4 30 2.0 35 70.31 0.809 17 50 1.0 40 72.81 0.927 5 30 2.5 40 67.19 0.843 18 50 1.5 20 80.65 0.643 6 35 0.5 25 78.85 0.472 19 50 2.0 25 77.89 0.725 7 35 1.0 30 76.20 0.637 20 50 2.5 30 72.33 0.869 8 35 1.5 35 74.37 0.819 21 70 0.5 40 62.79 0.915 9 35 2.0 40 68.50 0.872 22 70 1.0 20 70.62 0.639 10 35 2.5 20 75.21 0.603 23 70 1.5 25 67.78 0.755 11 40 0.5 30 80.32 0.631 24 70 2.0 30 63.93 0.859 12 40 1.0 35 76.29 0.759 25 70 2.5 35 57.99 1.082 13 40 1.5 40 70.20 0.872
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表 5 回歸系數評價表
Table 5. Regression coefficient evaluations
Correlation coefficient, r2 F value Probability corresponding to F value, P Variance of residuals 0.9841 102.8610 7.7×10?11 0.8132
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中文字幕在线观看表 6 參數優化結果
Table 6. Parameter optimization results
Vibration frequency/Hz Amplitude/mm Mesh inclination/(°) Theoretical screening efficiency/% Screening efficiency in simulation/% Average transport speed in simulation/(m?s?1) 51 0.6 27 81.01 81.49 0.732
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